Publication: Existence and uniqueness of solutions to the Bellman equation in stochastic dynamic programming
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2022-06-29
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Abstract
In this paper we develop a general framework to analyze stochastic dynamic optimization problems in discrete time. We obtain new results of the existence and uniqueness of solutions to the Bellman equation through a general xed point theorem that generalizes known results for Banach contractions and local contractions. We study an endogenous growth model as well as the Lucas asset pricing model in an exchange economy, signicantly expanding their range of applicability.
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Stochastic Dynamic Programming, Contraction Mapping, Bellman Equation, Value Function, Endogenous Growth, Asset Pricing Model